This invention relates to a high-accuracy quadrature multipath mass flow meter system and method for measuring mass flow rate.
Quadrature multipath mass flow meter systems are used to fairly accurately determine the total mass flow rate of a fluid flowing in a conduit using quadrature integration of the product of the average fluid density xcfx81avg and the measured fluid velocity in each quadrature plane. See U.S. Pat. Nos. 3,564,912; 5,515,733; 6,047,602; and 4,300,401 incorporated herein by this reference.
In the prior art, the fluid velocities V1, V2, and V3 (assuming 3 parallel quadrature planes) are calculated using ultrasonic transducers which detect the transit times of ultrasonic pulses transmitted bidirectionally through the fluid in each of the three quadrature planes. The fluid velocities in each quadrature plane are then computed as a function of the transit times of the ultrasonic energy both with and against the direction of the flow. The transit times themselves are principally a function of the paths and the speed of sound in the fluid which, in turn, is a function of the density of the fluid. Factors which influence sound speed, other than density, are dealt with below. Once the fluid velocities are calculated, quadrature integration is used to calculate the volumetric flow rate Q. if density were uniform, one could calculate the fluid""s mass flow rate based on the products xcfx81avgV1, xcfx81avgV2, and xcfx81avgV3. In this case, the average density of the fluid xcfx81avg is measured, calculated, or assumed based on the fluid composition and conditions if it is known.
In many situations, however, the assumption that the density of the fluid in the conduit is uniform is erroneous. Temperature variations, elbows in the conduit (which act like centrifuges), and other factors can result in non-uniform density distributions in the conduit.
To illustrate the error associated with assuming that the density of the fluid in the conduit is uniform when in fact the density is different in each quadrature plane, suppose (using consistent units) that V1=3, V2=7, and V3=9 and the density is assumed to be uniform and of numerical value xcfx81avg=5.3. The average velocity is 6.33 and so the product of the averages is 33.5. But, if in reality the density is non-uniform such that the density of the fluid in each quadrature plane is different, for example, xcfx811=2, xcfx812=6, xcfx813=8, then the average density is still 5.3, but the average of the products is now (xcfx811V1+xcfx812V2+xcfx813V3)/3=40, not 33.5. Thus, using an average density and assuming the density is uniform when it is not generally results in an erroneous total mass flow rate calculation. This error occurs despite using quadrature integration or other methods which are generally perceived to yield accurate volumetric flow rate Q, and generally further assumed to yield an accurate mass flowrate when Q is multiplied by an average value for density, with density typically computed based on point measurement of temperature in the fluid and pressure measured near the wall of the conduit.
Such an error can be extremely important in many industries including the use of mass flow rate systems to determine the price to be paid for expensive commodities such as oil or even water.
It is therefore an object of this invention to provide a more accurate quadrature multipath mass flow meter system and method.
It is a further object of this invention to provide such a system and method which is accurate to within 0.5-1% in general industrial process control situations, and 0.25 to 0.5% in custody transfer applications.
It is a further object of this invention to provide such a system and method which reduces the error associated with the prior art wherein the density of the fluid (liquid or gas, or some multiphase mixtures) was assumed to be uniform.
It is a further object of this invention to provide such a system and method which can be used in cases where the density of the fluid varies within a conduit.
The invention results from the realization that a more accurate quadrature multipath mass flow meter system and method especially useful in connection with fluid flows having non-uniform density distributions is effected by not by taking the product of the average fluid density and the volumetric flowrate Q determined by quadrature integration of the fluid velocities in each quadrature plane, but, instead, by quadrature integration of the product of the fluid densities and the fluid velocities in each quadrature plane, to calculate the total mass flow rate of the fluid. The new method is more accurate because it a) eliminates errors associated with assuming that the density of the fluid in the conduit is uniform, or b) eliminates the errors associate with multiplying an accurate Q by an average density of an acknowledged or known density gradient and taking that xe2x80x9cproduct of the averagesxe2x80x9d to be the mass flowrate.
This invention features a method of analyzing and determining the mass flow rate of a fluid flowing in a conduit, the method comprising transmitting ultrasonic energy along multiple xe2x80x9cv pathsxe2x80x9d in multiple parallel quadrature planes through the fluid, measuring the transit time of the ultrasonic energy through the fluid with and against the flow direction of the fluid, calculating the flow velocity of the fluid in each quadrature plane based on the transit time in each quadrature plane, determining the density of the fluid in each quadrature plane, and performing quadrature integration of the product of the fluid density and fluid velocity in each quadrature plane to calculate the total mass flow rate of the fluid more accurately by eliminating errors associated with assuming that the density of the fluid in the conduit is uniform.
In one embodiment, the density is determined in each quadrature plane by calculating the speed of sound in each quadrature plane from the transit time of the ultrasonic energy through the fluid in each quadrature plane and referencing a library including speed of sound and density data for different fluids.
In other embodiments, the density of the fluid is determined by measuring the density of the fluid. In one example, the density of the fluid in each quadrature plane is measured by transmitting ultrasonic energy as a torsional wave in a waveguide sensor located in each of the quadrature planes, measuring the transit time of the ultrasonic energy in the fluid, and calculating the density of the fluid in each quadrature plane based on the transit time in each quadrature plane. In another example, the density of the fluid in a first quadrature plane is measured by transmitting ultrasonic energy in the first quadrature plane, measuring the transit time of the ultrasonic energy in the fluid in the quadrature plane, calculating the density of the fluid in the first quadrature plane based on the transit time of the ultrasonic energy in the first quadrature plane, and deriving, using Rao""s rule, for example, the density of the fluid in the other quadrature planes from the measured density of the fluid in the first quadrature plane.
Typically, for the fluid velocity measurements, the ultrasonic energy is transmitted across each quadrature plane and then reflected back across each quadrature plane, and the parallel quadrature planes extend horizontally.
Further included may be the steps of measuring the temperature and pressure of the fluid and calculating the mass flow rate using the temperature and pressure measurements.
In still another example, the speed of sound is calculated based on the transit time of the ultrasonic energy through the fluid and the density of the fluid in each quadrature plane is determined using the calculated speed of sound in each quadrature plane.
A higher accuracy quadrature mass flow meter in accordance with this invention features a first set of ultrasonic transducers aligned to transmit ultrasonic energy along multiple paths in multiple parallel quadrature planes through a fluid flowing in a conduit, a second set of ultrasonic transducers aligned in the quadrature planes to receive the ultrasonic energy transmitted by the first set, means for determining the density of the fluid in each quadrature plane, and an electronic subsystem responsive to the ultrasonic transducers and the means for determining density, the electronic subsystem configured to calculate the flow velocity of the fluid in each quadrature plane based on the transit time of the transmitted ultrasonic energy in each quadrature plane, the electronics subsystem including a processor programmed to perform quadrature integration of the product of the fluid density and fluid velocity in each quadrature plane and to calculate the total mass flow rate of the fluid.
In one embodiment, the means includes a memory including speed of sound and density data for different liquids and the processor is configured to calculate the speed of sound in each quadrature plane from the transit time of the transmitted ultrasonic energy through the fluid in each quadrature plane, and to compare the calculated speed of sound in each quadrature plane with the data in the memory to determine the density of the fluid in each quadrature plane.
In another embodiment, the means includes a third plurality of ultrasonic transducers located downstream from the second plurality of transducers and also aligned with the quadrature planes and configured to transmit ultrasonic energy in the fluid. In this embodiment, the processor is programmed to calculate the density of the fluid in each quadrature plane based on the transit time of the ultrasonic energy in the fluid transmitted by the third plurality of transducers. Typically, the third plurality of transducers are each configured to launch a torsional wave in an acoustic waveguide in the fluid, and the third plurality of transducers each include a waveguide extending through the conduit.
In another embodiment, the density measuring means includes a single ultrasonic transducer located downstream from the second plurality of transducers aligned with a first quadrature plane and configured to transmit ultrasonic energy in a waveguide sensor in the fluid in said first quadrature plane. The processor is then programmed to calculate the density of the fluid in the first quadrature plane based on the transit time of the ultrasonic energy in the sensor portion of the waveguide immersed in the fluid transmitted by the single ultrasonic transducer and to derive the density of the fluid in the other quadrature planes based on the calculated density of the fluid in the first quadrature plane using, for example, Rao""s rule.
In one example, the conduit is a spoolpiece including all of the transducers disposed therein and coupled or installed between two conduit sections. Typically, the parallel quadrature planes extend horizontally, the first and second set of ultrasonic transducers are located on the same side of the conduit, and a set of reflectors are disposed on the opposite side of the conduit between the first and second set of ultrasonic transducers for redirecting ultrasonic energy from one set of transducers to the other. Also, the quadrature planes are typically perpendicular to a transverse axis of the conduit. In one specific example, each ultrasonic transducer is installed in a fitting located in an insert attached to the conduit, and the insert forms a truncated cone whose vertex is coincident with intersection of the longitudinal axis of the insert and the interior wall of the conduit.
Further included may be temperature and pressure sensors for detecting temperatures and pressure of the fluid in the conduit. Also, it may be preferable that the first and second sets of transducers are aligned such that all of the ultrasonic energy interactions with the fluid occur in a volume defined by planes at the end of a cube inscribed in the conduit.